System Reduction Method Research Articles

Comparative analysis of waste reduction methods for sustainable manufacturing systems using concurrent triangulation model

The aim of this study is to carry out a comparative analysis of waste reduction methods for sustainable manufacturing systems using Cronbach alpha and concurrent triangulation model. The objective of this research is to establish an ideal sustainable manufacturing waste disposal method. Reliability test results showed that the Cronbach alpha values used to measure the internal consistency of responses recorded for recycling, reuse, reduce, remanufacture and landfilling were 0.8160 , 0.8100 , 0.7760 , 0.7550 and 0.7340 respectively with recycling recording the highest internal consistency. The concurrent triangulation model recorded results showed that recycling recorded a total of 184 respondents at the highest percentage of 51.11 %, reuse recorded a total of 58 respondents with 16.13 %, remanufacture recorded 43 respondents at 11.94%, reduce recorded a total of 38 respondents at 10.55 %, and Landfilling had 37 respondents with 10.27 %. Hence Recycling was selected as the most appropriate method.
 Keywords: Concurrent Triangulation model, cronbach alpha, Recycling, Reuse, Remanufacturing, Sustainable manufacturing system.

Model order reduction based on discrete-time Laguerre functions for discrete linear periodic time-varying systems

Many engineering problems can be modelled as linear periodic time-varying (LPTV) systems, which naturally leads to the need for model order reduction of LPTV systems. This paper investigates a new model order reduction method for discrete LPTV systems. First, the state-space realization in the Fourier-lifted form of discrete LPTV system is constructed by representing periodic matrices in exponentially modulated periodic (EMP) Fourier series. By using Laguerre functions to expand the transfer function of the resulting Fourier-lifted system, the corresponding model order reduction algorithm is developed. Furthermore, the proposed algorithm is used to reduce the discrete LPTV system in the standard-lifted form. Theoretical analysis indicates that the transfer functions of both reduced order systems can match a certain number of moments. Finally, two numerical examples are given to verify the effectiveness of the proposed method.

A dynamic order reduction method for fluid-structure systems

In this paper, an iterative method is proposed to reduce the order of the coupled eigenvalue problem related to fluid-structure interaction systems. In fact, it is required to solve a smaller eigenvalue problem rather than the larger one (original) to compute the natural frequencies and mode shapes of the system. To this end, all degrees of freedom (DOFs) of the system are divided into master (retained) and slave (eliminated) ones. Then, the problem is re-expressed based on the master DOFs and a transformation matrix is introduced. The results show a remarkable decline in computational costs, whereas the accuracy of the modal outputs does not significantly decrease. A stopping criterion is defined to check whether the iterative process converges. Moreover, three fluid-structure systems are analyzed, including a two-dimensional fully-filled concrete tank, a two-dimensional gravity dam-reservoir, and a three-dimensional arch dam-reservoir, to assess the correctness and performance of the presented method. Findings prove that the proposed method is able to reduce the order of the eigenvalue problem of fluid-structure systems.

Design of modular concrete heliostats using symmetry reduction methods

AbstractIn Concentrated Solar Power (CSP) plants the incident solar radiation is focused onto a receiver by means of collectors. A fluid is heated up and in a downstream power block electricity is generated. In point‐focusing solar towers, the solar concentration is achieved by so‐called heliostats that are arranged to a solar field. In this contribution, the development of concrete heliostats with circular shapes and an aperture area of 30 m2 is presented. A high‐performance concrete with high tensile and compressive strength values is used. The circular structure is dissolved into identical but symmetrically reduced modules derived from system reduction methods. For designing, the tensile strength of the concrete is restrictive to ensure linear‐elastic material behavior and to avoid softening by cracking. After dimensioning, the derived equivalent plate is converted into strut‐like structures possessing equal stiffnesses with respect to the partial module size. These modules are circularly post‐tensioned to form a heliostat. Numerical investigations of the modules prove their accuracy. A full solar concentration, that is, the reflected solar radiation is completely focused on the receiver, is achieved. Due to the multitude of modules within a solar field, serial production with integrated quality control is recommended.

Time domain and frequency domain model order reduction for discrete time-delay systems

This paper explores model order reduction (MOR) methods for discrete time-delay systems in the time domain and the frequency domain. First, the discrete time-delay system is expanded under discrete Laguerre polynomials, and the discrete Laguerre coefficients of the system are obtained by a matrix equation. After that, the reduced order system is obtained by using the projection matrix based on these coefficients. Theoretical analysis shows that the resulting reduced order system can preserve a certain number of discrete Laguerre coefficients of output variables in the time domain. We also derive the error bound in the time domain. Furthermore, in order to obtain the moments of the system, we approximate the transfer function of the discrete time-delay system by Taylor expansion. The basis matrices of the higher order Krylov subspace are deduced by a iterative process. Further, we prove that the reduced order system can match a desired number of moments of the original system. The error estimation is obtained in the frequency domain. Finally, two illustrative examples are given to verify the effectiveness of the proposed methods.

$$\varepsilon $$-Embedding Model Reduction Method for Time-Delay Differential Algebra Systems

A new model order reduction (MOR) method for large-scale time-delay differential algebra systems is proposed herein. The presented MOR algorithm is based on parametric moment matching and $$\varepsilon $$ -embedding. By selecting an appropriate projection matrix, this process generates reduced-order models that preserve the structure of the original time-delay differential algebra system. Additionally, moment-matching results and error estimations are provided. Finally, two numerical circuits are tested to illustrate the effectiveness of the proposed MOR method.

Data-Driven Model Reduction of Monotone Systems by Nonlinear DC Gains

In this paper, we develop data-driven model reduction methods for monotone nonlinear control systems based on a nonlinear version of the dc gain. The nonlinear dc gain is a function of the amplitude of the input and can be used to evaluate the importance of each state variable. In fact, the nonlinear dc gain is directly related to the infinity-induced norm of the system as well as a notion of output reachability. Given the dc gain, model reduction is performed by either truncating not-so-important state variables or aggregating state variables having similar importance. Under such truncation and clustering, monotonicity and boundedness of the nonlinear dc gain are preserved; moreover, these two operations can be approximately performed based on simulation or experimental data alone. This empirical model reduction approach is illustrated by an example of a gene regulatory network.

Hankel-norm approximation of large-scale descriptor systems

Hankel-norm approximation is a model reduction method for linear time-invariant systems, which provides the best approximation in the Hankel semi-norm. In this paper, the computation of the optimal Hankel-norm approximation is generalized to the case of linear time-invariant continuous-time descriptor systems. A new algebraic characterization of all-pass descriptor systems is developed and used to construct an efficient algorithm by refining the generalized balanced truncation square root method. For a wide practical usage, adaptations of the introduced algorithm towards stable computations and sparse systems are suggested, as well as an approach for a projection-free algorithm. To show the approximation behavior of the introduced method, numerical examples are presented.

Truncated model reduction methods for linear time-invariant systems via eigenvalue computation

This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

Constructing reduced model for complex physical systems via interpolation and neural networks* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11871400 and 11971386) and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2017JM1019).

The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate the nonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation before approximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic mode decomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, a novel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid of error data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy. Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.

Model reduction by balanced truncation of dominant Lure systems

The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for non-equilibrium behaviors. The proposed framework addresses this need by exploiting recent advances on dominance theory. Classical balanced truncation for linear time-invariant systems is used to develop a dominance-preserving model reduction method for Lure systems, i.e.systems that can be decomposed as the feedback interconnection of a linear system and a static nonlinearity. The method is illustrated by approximating the oscillatory behavior of a discretized heat flow control system.

A time-varying Gramian based model reduction approach for Linear Switched Systems

We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example.

Model reduction of controlled Fokker–Planck and Liouville–von Neumann equations

Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker--Planck type. Methods based on balancing generalized system Gramians and on minimizing an H2-type cost functional are considered. The focus is on the numerical implementation and a thorough comparison of the methods. Structure and stability preservation are investigated, and the competitiveness of the approaches is shown for practically relevant, large-scale examples.

Radiometric calibration of thermal emission data from the Asteroid and Lunar Environment Chamber (ALEC).

The vacuum and thermal environment of airless planetary surfaces, particularly those dominated by a particulate regolith such as the Moon and asteroids, produces intense near-surface thermal gradients that can substantially alter their thermal emissivity spectra when compared with spectra collected at ambient terrestrial conditions. Therefore, spectroscopic measurements acquired under conditions designed to simulate the radiation environment in which remote measurements of airless bodies are made should be used as the basis for interpreting those data. As a foundation for this goal, we report the radiometric calibration of thermal infrared emission data collected with a Fourier transform infrared spectrometer integrated with the custom Asteroid and Lunar Environment Chamber (ALEC) at Brown University. This chamber is designed to simulate the environment of airless planetary bodies by evacuating the atmospheric gasses to vacuum (<10-4 mbar), cooling the chamber with a flow of liquid nitrogen, heating the base and sides of samples with temperature-controlled sample cups, and heating the top of samples with an external light source. We present a new method for deriving sample emissivity based on the absolute radiometry properties of our system, focusing on the 400-2000 cm-1 wavenumber range. This method produces calibrated radiance spectra from calibration targets, and particulate samples and those spectra are used to derive emissivity spectra. We demonstrate that the ALEC system and data reduction methods successfully replicate independently determined spectral properties of particulate samples under both ambient and cold, vacuum conditions. The ALEC system is shown to be capable of supporting ongoing and future planetary exploration of airless surfaces by facilitating careful investigation of meteorites, lunar samples, and planetary materials at an array of environmental conditions.

Index System Reduction Method Based on the Index Similarity

Index System Reduction Method Based on the Index Similarity

Comparative Verification of Radiation Noise Reduction Effect Using Spread Spectrum for Inductive Power Transfer System

This paper provides a comparative study on radiation noise reduction methods for inductive power transfer systems using spread spectrum. In the spread spectrum methods, the radiation noise is reduced by continuously changing an output frequency of the inverter according to pseudorandom numbers. The effects of the radiation noise reduction are evaluated with the inductive power transfer (IPT) system with series-parallel compensation and series-series compensation. The results show that the peak values of the radiation noise around the fundamental frequency are reduced by 7.8 and 8.1 dBμA in maximum with the series-series compensation method and the series-parallel compensation method, respectively in comparison with the constant frequency operation. From these results, the proposed methods are effective for both the series-series compensation and series-parallel compensation method. Moreover, the efficiency of the IPT system with spread spectrum method is evaluated. The maximum DC-to-DC efficiency with the spread spectrum is 94.1% and 92.0% with the series-series compensation and the series-parallel compensation, respectively.

Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of auxiliary variables. The lifted model is equivalent to the original model; it uses a change of variables but introduces no approximations. When discretized, the lifted model yields a polynomial system of either ordinary differential equations or differential-algebraic equations, depending on the problem and lifting transformation. Proper orthogonal decomposition (POD) is applied to the lifted models, yielding a reduced-order model for which all reduced-order operators can be precomputed. Thus, a key benefit of the approach is that there is no need for additional approximations of nonlinear terms, which is in contrast with existing nonlinear model reduction methods requiring sparse sampling or hyper-reduction. Application of the lifting and POD model reduction to the FitzHugh–Nagumo benchmark problem and to a tubular reactor model with Arrhenius reaction terms shows that the approach is competitive in terms of reduced model accuracy with state-of-the-art model reduction via POD and discrete empirical interpolation while having the added benefits of opening new pathways for rigorous analysis and input-independent model reduction via the introduction of the lifted problem structure.

Order Reduction in Linear Dynamical Systems by Using Improved Balanced Realization Technique

In this article, a new model order reduction scheme is proposed for the simplification of large-scale linear dynamical models. The proposed technique is based on the balanced realization method, in which the steady-state gain problem of the balanced truncation is circumvented. In this method, the denominator coefficients of the reduced system are evaluated by using the balanced realization, and the numerator coefficients are obtained by using a simple mathematical procedure as given in the literature. The proposed technique has been illustrated through some standard large-scale systems. This method gives the least performance error indices compared to some other existing system reduction methods. The time response of the approximated system, evaluated by the proposed method, is also shown which is the excellent matching of the response of the actual model when compared to the responses of other existing techniques.

Finite-time balanced truncation for linear systems via shifted Legendre polynomials

In this paper, we present a finite-time model order reduction method for linear systems via shifted Legendre polynomials. The main idea of the approach is to use finite-time empirical Gramians, which are constructed from impulse responses by solving block tridiagonal linear systems, to generate approximate balanced system for the large-scale system. The balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted Legendre polynomials, without individual reduction of the Gramians and a separate eigenvector solve. Then, the reduced-order model is constructed by truncating the states corresponding to the small approximate Hankel singular values (HSVs). The stability preservation of the reduced model is briefly discussed. And in combination with the dominant subspace projection method, we modify the reduction procedure to alleviate the shortcomings of the above method, which may unexpectedly lead to unstable systems even though the original one is stable. Furthermore, the properties of the resulting reduced models are considered. Finally, numerical experiments are given to demonstrate the effectiveness of the proposed methods.

Time-limited [formula omitted]-optimal model order reduction

In this paper, we investigate a time-limited H2-model order reduction method for linear dynamical systems. For this, we propose a time-limited H2-norm and show its connection with the time-limited Gramians. We then derive first-order conditions for optimality of reduced-order systems with respect to the time-limited H2-norm. Based on these optimality conditions, we propose an iterative correction scheme to construct reduced-order systems, which, upon convergence, nearly satisfy these conditions. Furthermore, a diagnostic measure is proposed for how close the obtained reduced-order system is to optimality. We test the efficiency of the proposed iterative scheme using various numerical examples and illustrate that the newly proposed iterative method can lead to a better reduced-order models compared to the unrestricted iterative rational Krylov subspace algorithm in a finite time interval of interest.